With regard to an electric power steering device for vehicles such as automobiles it is known as described in Japanese Patent Publication No. 2690230 (Japanese Patent Laid-open Publication Hei 5-124524) to provide a screw at a part of a linearly and rotationally movable tie rod connecting bar pivotably connected with tie rods at opposite ends thereof, and to let the tie rod connecting bar move leftward or rightward according to a turning operation of a steering shaft by driving a nut engaged around the screw, while to provide a spline at a part of the tie rod connecting bar and to selectively drive a spline nut engaging the spline by an electric motor so that the tie rod connecting bar is driven in its axial direction at the screw portion when it is rotated by the driving force of the electric motor via the spline nut.